If tan2A = cot(A - 18°), where 2A is an acute angle, find the value of A.

Given tan2A = cot(A - 18°)
→ cot(90° - 2A) = cot(A - 18°) [∵ tan θ = cot(90° - θ)]
Comparing angles we get
90° - 2A = A - 18°
→ 90° + 18° = A + 2A
→ 3A = 108°
→ A = 108°/3
→ A = 36°